New answers tagged lo.logic
0
Version 1.5 of Lisp (1955) supports homoiconicity. It's not a model of computation but it could still be interesting.
Sidenote: I wrote an implementation of Lisp 1.5 that supports homoiconicity.
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A something that might be too long for a comment, based on the previous answer by Emil.
In the case you are interested in the complexity of such a logic, consider reading LICS'2015 paper by Joël Ouaknine, Antonia Lechner and Ben Worrell. A preprint is available here: https://www.cs.ox.ac.uk/people/james.worrell/LICS-main.pdf
According to the authors, the ...
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($=$ is a logical symbol, hence I will not write it as part of the signature.) The satisfiability problem is decidable, as $\gcd$ has both a universal and an existential definition in terms of $|$, $+$, and $\le$:
$$\begin{align*}
\gcd(a,b)=c&\iff c\ge0\land c\mid a\land c\mid b\land\forall d\:(d\mid a\land d\mid b\to d\mid c)\\
&\iff c\ge0\land c\...
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